I learned that only 36% of astronauts have earned doctorate degrees, but most of the astronauts selected with only a masters or bachelors had extensive NASA and/or military experience. The typical astronaut has one bachelors and one masters degree, although some do have more than one of either type of degree, with the most being 2 bachelors and 3 masters. Some other tidbits of note are that 4 astronauts have MBAs, 1 has a DVM, and only 1 has a MD/Ph.D.
I suspect the percentage of astronauts with military experience would go up if I included the larger pool or former astronauts too, since in the pre-shuttle era, nearly all astronauts were military. However, the current pool has a 60/40 split, meaning it's still beneficial to have a military background, but it's not a must.